The former Lyon striker played with Terry at Chelsea.
He told Villa's website: “I played with JT at Chelsea, I spoke to him.
“I spoke to the Manager, spoke with the Sporting Director as well and some players I used to play with – Nakamba and El Ghazi.
“I spoke to Nakamba, I talked to him a little bit about the club.
“Many things made me take the decision to come here.
Traore also remarked: “I'm excited to be back (in England). I always wanted to come back to the Premier League.
“I had to follow my own way as well and gain some more experience.
“I think it is the right time to come back.
“I think I'm coming back as a better player, with more experience.
“And this is the right place for me to come back. It's good."